#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_011 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(530,7620,25200,30180,12072) ### ### H_*=(Z,0,0,0,Z) ### ### PL 4-sphere ### ### ### ### ### ### references: ### ### ### ### Frank H. Lutz and Mimi Tsuruga. ### ### Constructing complicated spheres. ### ### arXiv:1302.6856[math.CO], 2013. ### ### ### ### ### #################################################################################### #################################################################################### #################################################################################### facets:=[ [0,1,2,5,353],[0,1,2,35,383],[0,1,2,350,353],[0,1,2,350,383], [0,1,4,5,353],[0,1,4,178,352],[0,1,4,352,353],[0,1,34,35,383], [0,1,34,166,340],[0,1,34,166,514],[0,1,34,208,340],[0,1,34,382,383], [0,1,34,382,514],[0,1,165,166,340],[0,1,165,166,514],[0,1,165,339,340], [0,1,165,339,513],[0,1,165,513,514],[0,1,175,178,352],[0,1,175,208,340], [0,1,175,339,340],[0,1,175,339,513],[0,1,349,350,353],[0,1,349,350,383], [0,1,175,349,352],[0,1,349,352,353],[0,1,349,382,383],[0,1,349,382,514], [0,1,175,349,513],[0,1,349,513,514],[0,2,5,26,200],[0,2,5,26,374], [2,5,26,200,374],[0,2,5,179,200],[2,5,179,200,374],[0,2,5,353,374], [2,5,179,353,374],[0,2,26,29,203],[0,2,26,29,377],[2,26,29,203,377], [0,2,26,200,203],[2,26,200,203,377],[0,2,26,374,377],[2,26,200,374,377], [0,2,29,169,343],[0,2,29,169,517],[0,2,29,203,343],[0,2,29,377,517], [0,2,35,169,343],[0,2,35,169,517],[0,2,35,209,343],[0,2,35,383,517], [0,2,176,179,200],[2,176,179,200,374],[2,176,179,353,374],[0,2,176,200,203], [2,176,200,203,377],[2,176,200,374,377],[0,2,176,203,343],[0,2,176,209,343], [0,2,350,353,374],[2,176,350,353,374],[0,2,350,374,377],[2,176,350,374,377], [0,2,350,377,517],[0,2,350,383,517],[0,3,4,5,353],[0,3,4,178,352], [0,3,4,352,353],[0,3,5,26,200],[0,3,5,26,374],[0,3,5,179,200], [0,3,5,353,374],[0,3,24,26,200],[0,3,24,26,374],[0,3,24,198,200], [0,3,24,198,372],[0,3,24,372,374],[0,3,177,178,352],[0,3,177,179,200], [0,3,177,198,200],[0,3,177,198,372],[0,3,177,351,352],[0,3,351,352,353], [0,3,351,353,374],[0,3,177,351,372],[0,3,351,372,374],[0,24,26,29,203], [0,24,26,29,377],[0,24,26,200,203],[0,24,26,374,377],[0,24,27,29,203], [0,24,27,29,377],[0,24,27,201,203],[0,24,27,201,375],[0,24,27,375,377], [0,24,198,200,203],[0,24,198,201,203],[0,24,198,201,375],[0,24,372,374,377], [0,24,198,372,375],[0,24,372,375,377],[0,27,29,169,343],[0,27,29,169,517], [0,27,29,203,343],[0,27,29,377,517],[0,27,162,166,340],[0,27,162,166,514], [0,27,162,169,343],[0,27,162,169,517],[0,27,162,336,340],[0,27,162,336,343], [0,27,162,510,514],[0,27,162,510,517],[0,27,165,166,340],[0,27,165,166,514], [0,27,165,339,340],[0,27,165,339,513],[0,27,165,513,514],[0,27,201,203,343], [0,27,201,336,340],[0,27,201,336,343],[0,27,201,339,340],[0,27,201,339,513], [0,27,375,377,517],[0,27,375,510,514],[0,27,375,510,517],[0,27,201,375,513], [0,27,375,513,514],[0,33,34,35,383],[0,33,34,166,340],[0,33,34,166,514], [0,33,34,208,340],[0,33,34,382,383],[0,33,34,382,514],[0,33,35,169,343], [0,33,35,169,517],[0,33,35,209,343],[0,33,35,383,517],[0,33,162,166,340], [0,33,162,166,514],[0,33,162,169,343],[0,33,162,169,517],[0,33,162,336,340], [0,33,162,336,343],[0,33,162,510,514],[0,33,162,510,517],[0,33,207,208,340], [0,33,207,209,343],[0,33,207,336,340],[0,33,207,336,343],[0,33,381,382,383], [0,33,381,382,514],[0,33,381,383,517],[0,33,381,510,514],[0,33,381,510,517], [174,175,176,179,353],[174,175,176,209,383],[174,175,176,350,353],[174,175,176,350,383], [174,175,178,179,353],[0,174,175,178,352],[174,175,178,352,353],[174,175,208,209,383], [0,174,175,208,340],[174,175,208,340,514],[174,175,208,382,383],[174,175,208,382,514], [0,174,175,339,340],[174,175,339,340,514],[0,174,175,339,513],[174,175,339,513,514], [174,175,349,350,353],[174,175,349,350,383],[0,174,175,349,352],[174,175,349,352,353], [174,175,349,382,383],[174,175,349,382,514],[0,174,175,349,513],[174,175,349,513,514], [0,174,176,179,200],[174,176,179,200,374],[174,176,179,353,374],[0,174,176,200,203], [174,176,200,203,377],[174,176,200,374,377],[0,174,176,203,343],[174,176,203,343,517], [174,176,203,377,517],[0,174,176,209,343],[174,176,209,343,517],[174,176,209,383,517], [174,176,350,353,374],[174,176,350,374,377],[174,176,350,377,517],[174,176,350,383,517], [174,177,178,179,353],[0,174,177,178,352],[174,177,178,352,353],[0,174,177,179,200], [174,177,179,200,374],[174,177,179,353,374],[0,174,177,198,200],[174,177,198,200,374], [0,174,177,198,372],[174,177,198,372,374],[0,174,177,351,352],[174,177,351,352,353], [174,177,351,353,374],[0,174,177,351,372],[174,177,351,372,374],[0,174,198,200,203], [174,198,200,203,377],[174,198,200,374,377],[0,174,198,201,203],[174,198,201,203,377], [0,174,198,201,375],[174,198,201,375,377],[174,198,372,374,377],[0,174,198,372,375], [174,198,372,375,377],[0,174,201,203,343],[174,201,203,343,517],[174,201,203,377,517], [0,174,201,336,340],[174,201,336,340,514],[0,174,201,336,343],[174,201,336,343,517], [174,201,336,510,514],[174,201,336,510,517],[0,174,201,339,340],[174,201,339,340,514], [0,174,201,339,513],[174,201,339,513,514],[174,201,375,377,517],[174,201,375,510,514], [174,201,375,510,517],[0,174,201,375,513],[174,201,375,513,514],[174,207,208,209,383], [0,174,207,208,340],[174,207,208,340,514],[174,207,208,382,383],[174,207,208,382,514], [0,174,207,209,343],[174,207,209,343,517],[174,207,209,383,517],[0,174,207,336,340], [174,207,336,340,514],[0,174,207,336,343],[174,207,336,343,517],[174,207,336,510,514], [174,207,336,510,517],[174,207,381,382,383],[174,207,381,382,514],[174,207,381,383,517], [174,207,381,510,514],[174,207,381,510,517],[0,348,349,350,353],[174,348,349,350,353], [0,348,349,350,383],[174,348,349,350,383],[0,174,348,349,352],[0,348,349,352,353], [174,348,349,352,353],[0,348,349,382,383],[174,348,349,382,383],[0,348,349,382,514], [174,348,349,382,514],[0,174,348,349,513],[0,348,349,513,514],[174,348,349,513,514], [0,348,350,353,374],[174,348,350,353,374],[0,348,350,374,377],[174,348,350,374,377], [0,348,350,377,517],[174,348,350,377,517],[0,348,350,383,517],[174,348,350,383,517], [0,174,348,351,352],[0,348,351,352,353],[174,348,351,352,353],[0,348,351,353,374], [174,348,351,353,374],[0,174,348,351,372],[0,348,351,372,374],[174,348,351,372,374], [0,348,372,374,377],[174,348,372,374,377],[0,174,348,372,375],[0,348,372,375,377], [174,348,372,375,377],[0,348,375,377,517],[174,348,375,377,517],[0,348,375,510,514], [174,348,375,510,514],[0,348,375,510,517],[174,348,375,510,517],[0,174,348,375,513], [0,348,375,513,514],[174,348,375,513,514],[0,348,381,382,383],[174,348,381,382,383], [0,348,381,382,514],[174,348,381,382,514],[0,348,381,383,517],[174,348,381,383,517], [0,348,381,510,514],[174,348,381,510,514],[0,348,381,510,517],[174,348,381,510,517], [1,2,5,41,215],[1,2,5,41,389],[2,5,41,215,389],[1,2,5,179,215], [2,5,179,215,389],[1,2,5,353,389],[2,5,179,353,389],[1,2,35,169,343], [1,2,35,169,517],[1,2,35,209,343],[1,2,35,383,517],[1,2,38,41,215], [1,2,38,41,389],[2,38,41,215,389],[1,2,38,172,346],[1,2,38,172,520], [1,2,38,212,215],[2,38,212,215,389],[1,2,38,212,346],[1,2,38,386,389], [2,38,212,386,389],[1,2,38,386,520],[1,2,168,169,343],[1,2,168,169,517], [1,2,168,172,346],[1,2,168,172,520],[1,2,168,342,343],[1,2,168,342,346], [1,2,168,516,517],[1,2,168,516,520],[1,2,176,179,215],[2,176,179,215,389], [2,176,179,353,389],[1,2,176,209,343],[1,2,176,212,215],[2,176,212,215,389], [1,2,176,212,346],[2,176,212,386,389],[1,2,176,342,343],[1,2,176,342,346], [1,2,350,353,389],[2,176,350,353,389],[1,2,350,383,517],[1,2,350,386,389], [2,176,350,386,389],[1,2,350,386,520],[1,2,350,516,517],[1,2,350,516,520], [1,4,5,41,215],[1,4,5,41,389],[1,4,5,179,215],[1,4,5,353,389], [1,4,39,41,215],[1,4,39,41,389],[1,4,39,213,215],[1,4,39,213,387], [1,4,39,387,389],[1,4,178,179,215],[1,4,178,213,215],[1,4,178,213,387], [1,4,352,353,389],[1,4,178,352,387],[1,4,352,387,389],[1,34,35,169,343], [1,34,35,169,517],[1,34,35,209,343],[1,34,35,383,517],[1,34,163,166,340], [1,34,163,166,514],[1,34,163,169,343],[1,34,163,169,517],[1,34,163,337,340], [1,34,163,337,343],[1,34,163,511,514],[1,34,163,511,517],[1,34,208,209,343], [1,34,208,337,340],[1,34,208,337,343],[1,34,382,383,517],[1,34,382,511,514], [1,34,382,511,517],[1,36,38,41,215],[1,36,38,41,389],[1,36,38,172,346], [1,36,38,172,520],[1,36,38,212,215],[1,36,38,212,346],[1,36,38,386,389], [1,36,38,386,520],[1,36,39,41,215],[1,36,39,41,389],[1,36,39,213,215], [1,36,39,213,387],[1,36,39,387,389],[1,36,163,166,340],[1,36,163,166,514], [1,36,163,169,343],[1,36,163,169,517],[1,36,163,337,340],[1,36,163,337,343], [1,36,163,511,514],[1,36,163,511,517],[1,36,165,166,340],[1,36,165,166,514], [1,36,165,339,340],[1,36,165,339,513],[1,36,165,513,514],[1,36,168,169,343], [1,36,168,169,517],[1,36,168,172,346],[1,36,168,172,520],[1,36,168,342,343], [1,36,168,342,346],[1,36,168,516,517],[1,36,168,516,520],[1,36,210,212,215], [1,36,210,212,346],[1,36,210,213,215],[1,36,210,213,387],[1,36,210,337,340], [1,36,210,337,343],[1,36,210,339,340],[1,36,210,339,513],[1,36,210,342,343], [1,36,210,342,346],[1,36,384,386,389],[1,36,384,386,520],[1,36,210,384,387], [1,36,384,387,389],[1,36,384,511,514],[1,36,384,511,517],[1,36,210,384,513], [1,36,384,513,514],[1,36,384,516,517],[1,36,384,516,520],[1,175,176,179,215], [175,176,179,215,389],[175,176,179,353,389],[1,175,176,209,343],[175,176,209,343,517], [175,176,209,383,517],[1,175,176,212,215],[175,176,212,215,389],[1,175,176,212,346], [175,176,212,346,520],[175,176,212,386,389],[175,176,212,386,520],[1,175,176,342,343], [175,176,342,343,517],[1,175,176,342,346],[175,176,342,346,520],[175,176,342,516,517], [175,176,342,516,520],[175,176,350,353,389],[175,176,350,383,517],[175,176,350,386,389], [175,176,350,386,520],[175,176,350,516,517],[175,176,350,516,520],[1,175,178,179,215], [175,178,179,215,389],[175,178,179,353,389],[1,175,178,213,215],[175,178,213,215,389], [1,175,178,213,387],[175,178,213,387,389],[175,178,352,353,389],[1,175,178,352,387], [175,178,352,387,389],[1,175,208,209,343],[175,208,209,343,517],[175,208,209,383,517], [1,175,208,337,340],[175,208,337,340,514],[1,175,208,337,343],[175,208,337,343,517], [175,208,337,511,514],[175,208,337,511,517],[175,208,382,383,517],[175,208,382,511,514], [175,208,382,511,517],[1,175,210,212,215],[175,210,212,215,389],[1,175,210,212,346], [175,210,212,346,520],[175,210,212,386,389],[175,210,212,386,520],[1,175,210,213,215], [175,210,213,215,389],[1,175,210,213,387],[175,210,213,387,389],[1,175,210,337,340], [175,210,337,340,514],[1,175,210,337,343],[175,210,337,343,517],[175,210,337,511,514], [175,210,337,511,517],[1,175,210,339,340],[175,210,339,340,514],[1,175,210,339,513], [175,210,339,513,514],[1,175,210,342,343],[175,210,342,343,517],[1,175,210,342,346], [175,210,342,346,520],[175,210,342,516,517],[175,210,342,516,520],[175,210,384,386,389], [175,210,384,386,520],[1,175,210,384,387],[175,210,384,387,389],[175,210,384,511,514], [175,210,384,511,517],[1,175,210,384,513],[175,210,384,513,514],[175,210,384,516,517], [175,210,384,516,520],[1,349,350,353,389],[175,349,350,353,389],[1,349,350,383,517], [175,349,350,383,517],[1,349,350,386,389],[175,349,350,386,389],[1,349,350,386,520], [175,349,350,386,520],[1,349,350,516,517],[175,349,350,516,517],[1,349,350,516,520], [175,349,350,516,520],[1,349,352,353,389],[175,349,352,353,389],[1,175,349,352,387], [1,349,352,387,389],[175,349,352,387,389],[1,349,382,383,517],[175,349,382,383,517], [1,349,382,511,514],[175,349,382,511,514],[1,349,382,511,517],[175,349,382,511,517], [1,349,384,386,389],[175,349,384,386,389],[1,349,384,386,520],[175,349,384,386,520], [1,175,349,384,387],[1,349,384,387,389],[175,349,384,387,389],[1,349,384,511,514], [175,349,384,511,514],[1,349,384,511,517],[175,349,384,511,517],[1,175,349,384,513], [1,349,384,513,514],[175,349,384,513,514],[1,349,384,516,517],[175,349,384,516,517], [1,349,384,516,520],[175,349,384,516,520],[2,29,168,169,343],[2,29,168,169,517], [2,29,168,172,346],[2,29,168,172,520],[2,29,168,342,343],[2,29,168,342,346], [2,29,168,516,517],[2,29,168,516,520],[2,29,170,172,346],[2,29,170,172,520], [2,29,170,344,346],[2,29,170,344,518],[2,29,170,518,520],[2,29,203,342,343], [2,29,203,342,346],[2,29,203,344,346],[2,29,203,344,518],[2,29,377,516,517], [2,29,377,516,520],[2,29,203,377,518],[2,29,377,518,520],[2,38,170,172,346], [2,38,170,172,520],[2,38,170,344,346],[2,38,170,344,518],[2,38,170,518,520], [2,38,212,344,346],[2,38,212,344,518],[2,38,212,386,518],[2,38,386,518,520], [2,176,203,342,343],[176,203,342,343,517],[2,176,203,342,346],[176,203,342,346,520], [176,203,342,516,517],[176,203,342,516,520],[2,176,203,344,346],[176,203,344,346,520], [2,176,203,344,518],[176,203,344,518,520],[176,203,377,516,517],[176,203,377,516,520], [2,176,203,377,518],[176,203,377,518,520],[2,176,212,344,346],[176,212,344,346,520], [2,176,212,344,518],[176,212,344,518,520],[2,176,212,386,518],[176,212,386,518,520], [2,350,377,516,517],[176,350,377,516,517],[2,350,377,516,520],[176,350,377,516,520], [2,176,350,377,518],[2,350,377,518,520],[176,350,377,518,520],[2,176,350,386,518], [2,350,386,518,520],[176,350,386,518,520],[3,4,5,8,356],[3,4,5,353,356], [3,4,7,8,356],[3,4,7,166,340],[3,4,7,166,514],[3,4,7,181,340], [3,4,7,355,356],[3,4,7,355,514],[3,4,165,166,340],[3,4,165,166,514], [3,4,165,339,340],[3,4,165,339,513],[3,4,165,513,514],[3,4,178,181,340], [3,4,178,339,340],[3,4,178,339,513],[3,4,352,353,356],[3,4,352,355,356], [3,4,352,355,514],[3,4,178,352,513],[3,4,352,513,514],[3,5,8,23,197], [3,5,8,23,371],[5,8,23,197,371],[3,5,8,182,197],[5,8,182,197,371], [3,5,8,356,371],[5,8,182,356,371],[3,5,23,26,200],[3,5,23,26,374], 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[27,29,203,206,522],[28,29,203,206,522],[28,31,32,206,522],[27,28,31,205,522], [28,31,205,206,522],[28,202,203,206,522],[27,28,202,205,522],[28,202,205,206,522], [27,30,32,206,522],[27,30,31,205,522],[27,30,204,205,522],[27,30,204,206,522], [27,201,203,206,522],[201,202,203,206,522],[27,201,202,205,522],[201,202,205,206,522], [27,201,204,205,522],[27,201,204,206,522],[201,204,205,206,522],[30,32,35,209,522], [31,32,35,209,522],[30,32,206,209,522],[31,32,206,209,522],[31,34,35,209,522], [30,31,34,208,522],[31,34,208,209,522],[31,205,206,209,522],[30,31,205,208,522], [31,205,208,209,522],[30,33,35,209,522],[30,33,34,208,522],[30,33,207,208,522], [30,33,207,209,522],[30,204,206,209,522],[204,205,206,209,522],[30,204,205,208,522], [204,205,208,209,522],[30,204,207,208,522],[30,204,207,209,522],[204,207,208,209,522], [0,1,2,5,523],[1,2,5,522,523],[0,1,2,35,523],[1,2,35,522,523], [0,1,4,5,523],[0,1,4,522,523],[1,4,5,522,523],[0,1,34,35,523], [0,1,34,522,523],[1,34,35,522,523],[0,3,4,5,523],[0,3,4,522,523], [0,33,34,35,523],[0,33,34,522,523],[3,4,5,8,523],[4,5,8,522,523], [3,4,7,8,523],[3,4,7,522,523],[4,7,8,522,523],[3,6,7,8,523], [3,6,7,522,523],[6,7,8,11,523],[7,8,11,522,523],[6,7,10,11,523], [6,7,10,522,523],[7,10,11,522,523],[6,9,10,11,523],[6,9,10,522,523], [9,10,11,14,523],[10,11,14,522,523],[9,10,13,14,523],[9,10,13,522,523], [10,13,14,522,523],[9,12,13,14,523],[9,12,13,522,523],[12,13,14,17,523], [13,14,17,522,523],[12,13,16,17,523],[12,13,16,522,523],[13,16,17,522,523], [12,15,16,17,523],[12,15,16,522,523],[15,16,17,20,523],[16,17,20,522,523], [15,16,19,20,523],[15,16,19,522,523],[16,19,20,522,523],[15,18,19,20,523], [15,18,19,522,523],[18,19,20,23,523],[19,20,23,522,523],[18,19,22,23,523], [18,19,22,522,523],[19,22,23,522,523],[18,21,22,23,523],[18,21,22,522,523], [21,22,23,26,523],[22,23,26,522,523],[21,22,25,26,523],[21,22,25,522,523], [22,25,26,522,523],[21,24,25,26,523],[21,24,25,522,523],[24,25,26,29,523], [25,26,29,522,523],[24,25,28,29,523],[24,25,28,522,523],[25,28,29,522,523], [24,27,28,29,523],[24,27,28,522,523],[27,28,29,32,523],[28,29,32,522,523], [27,28,31,32,523],[27,28,31,522,523],[28,31,32,522,523],[27,30,31,32,523], [27,30,31,522,523],[30,31,32,35,523],[31,32,35,522,523],[30,31,34,35,523], [30,31,34,522,523],[31,34,35,522,523],[30,33,34,35,523],[30,33,34,522,523], [0,2,5,522,524],[0,2,5,523,524],[2,5,522,523,524],[0,2,35,522,524], [0,2,35,523,524],[2,35,522,523,524],[0,3,5,522,524],[0,3,5,523,524], [0,33,35,522,524],[0,33,35,523,524],[3,5,8,522,524],[3,5,8,523,524], [5,8,522,523,524],[3,6,8,522,524],[3,6,8,523,524],[6,8,11,522,524], [6,8,11,523,524],[8,11,522,523,524],[6,9,11,522,524],[6,9,11,523,524], [9,11,14,522,524],[9,11,14,523,524],[11,14,522,523,524],[9,12,14,522,524], [9,12,14,523,524],[12,14,17,522,524],[12,14,17,523,524],[14,17,522,523,524], [12,15,17,522,524],[12,15,17,523,524],[15,17,20,522,524],[15,17,20,523,524], [17,20,522,523,524],[15,18,20,522,524],[15,18,20,523,524],[18,20,23,522,524], [18,20,23,523,524],[20,23,522,523,524],[18,21,23,522,524],[18,21,23,523,524], [21,23,26,522,524],[21,23,26,523,524],[23,26,522,523,524],[21,24,26,522,524], [21,24,26,523,524],[24,26,29,522,524],[24,26,29,523,524],[26,29,522,523,524], [24,27,29,522,524],[24,27,29,523,524],[27,29,32,522,524],[27,29,32,523,524], [29,32,522,523,524],[27,30,32,522,524],[27,30,32,523,524],[30,32,35,522,524], [30,32,35,523,524],[32,35,522,523,524],[30,33,35,522,524],[30,33,35,523,524], [0,3,522,523,525],[0,3,522,524,525],[0,3,523,524,525],[0,33,522,523,525], [0,33,522,524,525],[0,33,523,524,525],[3,6,522,523,525],[3,6,522,524,525], [3,6,523,524,525],[6,9,522,523,525],[6,9,522,524,525],[6,9,523,524,525], [9,12,522,523,525],[9,12,522,524,525],[9,12,523,524,525],[12,15,522,523,525], [12,15,522,524,525],[12,15,523,524,525],[15,18,522,523,525],[15,18,522,524,525], [15,18,523,524,525],[18,21,522,523,525],[18,21,522,524,525],[18,21,523,524,525], [21,24,522,523,525],[21,24,522,524,525],[21,24,523,524,525],[24,27,522,523,525], [24,27,522,524,525],[24,27,523,524,525],[27,30,522,523,525],[27,30,522,524,525], [27,30,523,524,525],[30,33,522,523,525],[30,33,522,524,525],[30,33,523,524,525], [36,38,41,215,526],[37,38,41,215,526],[36,38,161,335,526],[37,38,161,335,526], [36,38,212,215,526],[37,38,212,215,526],[36,38,212,335,526],[37,38,212,335,526], [37,40,41,215,526],[36,37,40,214,526],[37,40,214,215,526],[37,160,161,335,526], [36,37,160,334,526],[37,160,334,335,526],[37,211,212,215,526],[37,211,212,335,526], [36,37,211,214,526],[37,211,214,215,526],[36,37,211,334,526],[37,211,334,335,526], [36,39,41,215,526],[36,39,40,214,526],[36,39,213,214,526],[36,39,213,215,526], [36,159,161,335,526],[36,159,160,334,526],[36,159,333,334,526],[36,159,333,335,526], [36,210,212,215,526],[210,211,212,215,526],[36,210,212,335,526],[210,211,212,335,526], [36,210,211,214,526],[210,211,214,215,526],[36,210,211,334,526],[210,211,334,335,526], [36,210,213,214,526],[36,210,213,215,526],[210,213,214,215,526],[36,210,333,334,526], [36,210,333,335,526],[210,333,334,335,526],[39,41,44,218,526],[40,41,44,218,526], [39,41,215,218,526],[40,41,215,218,526],[40,43,44,218,526],[39,40,43,217,526], [40,43,217,218,526],[40,214,215,218,526],[39,40,214,217,526],[40,214,217,218,526], [39,42,44,218,526],[39,42,43,217,526],[39,42,216,217,526],[39,42,216,218,526], [39,213,215,218,526],[213,214,215,218,526],[39,213,214,217,526],[213,214,217,218,526], [39,213,216,217,526],[39,213,216,218,526],[213,216,217,218,526],[42,44,47,221,526], [43,44,47,221,526],[42,44,218,221,526],[43,44,218,221,526],[43,46,47,221,526], [42,43,46,220,526],[43,46,220,221,526],[43,217,218,221,526],[42,43,217,220,526], [43,217,220,221,526],[42,45,47,221,526],[42,45,46,220,526],[42,45,219,220,526], [42,45,219,221,526],[42,216,218,221,526],[216,217,218,221,526],[42,216,217,220,526], [216,217,220,221,526],[42,216,219,220,526],[42,216,219,221,526],[216,219,220,221,526], [45,47,50,224,526],[46,47,50,224,526],[45,47,221,224,526],[46,47,221,224,526], [46,49,50,224,526],[45,46,49,223,526],[46,49,223,224,526],[46,220,221,224,526], [45,46,220,223,526],[46,220,223,224,526],[45,48,50,224,526],[45,48,49,223,526], [45,48,222,223,526],[45,48,222,224,526],[45,219,221,224,526],[219,220,221,224,526], [45,219,220,223,526],[219,220,223,224,526],[45,219,222,223,526],[45,219,222,224,526], [219,222,223,224,526],[48,50,53,227,526],[49,50,53,227,526],[48,50,224,227,526], [49,50,224,227,526],[49,52,53,227,526],[48,49,52,226,526],[49,52,226,227,526], [49,223,224,227,526],[48,49,223,226,526],[49,223,226,227,526],[48,51,53,227,526], [48,51,52,226,526],[48,51,225,226,526],[48,51,225,227,526],[48,222,224,227,526], [222,223,224,227,526],[48,222,223,226,526],[222,223,226,227,526],[48,222,225,226,526], [48,222,225,227,526],[222,225,226,227,526],[51,53,56,230,526],[52,53,56,230,526], [51,53,227,230,526],[52,53,227,230,526],[52,55,56,230,526],[51,52,55,229,526], [52,55,229,230,526],[52,226,227,230,526],[51,52,226,229,526],[52,226,229,230,526], [51,54,56,230,526],[51,54,55,229,526],[51,54,228,229,526],[51,54,228,230,526], [51,225,227,230,526],[225,226,227,230,526],[51,225,226,229,526],[225,226,229,230,526], [51,225,228,229,526],[51,225,228,230,526],[225,228,229,230,526],[54,56,59,233,526], [55,56,59,233,526],[54,56,230,233,526],[55,56,230,233,526],[55,58,59,233,526], [54,55,58,232,526],[55,58,232,233,526],[55,229,230,233,526],[54,55,229,232,526], [55,229,232,233,526],[54,57,59,233,526],[54,57,58,232,526],[54,57,231,232,526], [54,57,231,233,526],[54,228,230,233,526],[228,229,230,233,526],[54,228,229,232,526], [228,229,232,233,526],[54,228,231,232,526],[54,228,231,233,526],[228,231,232,233,526], [57,59,62,236,526],[58,59,62,236,526],[57,59,233,236,526],[58,59,233,236,526], [58,61,62,236,526],[57,58,61,235,526],[58,61,235,236,526],[58,232,233,236,526], [57,58,232,235,526],[58,232,235,236,526],[57,60,62,236,526],[57,60,61,235,526], [57,60,234,235,526],[57,60,234,236,526],[57,231,233,236,526],[231,232,233,236,526], [57,231,232,235,526],[231,232,235,236,526],[57,231,234,235,526],[57,231,234,236,526], [231,234,235,236,526],[60,62,65,239,526],[61,62,65,239,526],[60,62,236,239,526], [61,62,236,239,526],[61,64,65,239,526],[60,61,64,238,526],[61,64,238,239,526], [61,235,236,239,526],[60,61,235,238,526],[61,235,238,239,526],[60,63,65,239,526], [60,63,64,238,526],[60,63,237,238,526],[60,63,237,239,526],[60,234,236,239,526], [234,235,236,239,526],[60,234,235,238,526],[234,235,238,239,526],[60,234,237,238,526], [60,234,237,239,526],[234,237,238,239,526],[63,65,68,242,526],[64,65,68,242,526], [63,65,239,242,526],[64,65,239,242,526],[64,67,68,242,526],[63,64,67,241,526], [64,67,241,242,526],[64,238,239,242,526],[63,64,238,241,526],[64,238,241,242,526], [63,66,68,242,526],[63,66,67,241,526],[63,66,240,241,526],[63,66,240,242,526], [63,237,239,242,526],[237,238,239,242,526],[63,237,238,241,526],[237,238,241,242,526], [63,237,240,241,526],[63,237,240,242,526],[237,240,241,242,526],[66,68,71,245,526], [67,68,71,245,526],[66,68,242,245,526],[67,68,242,245,526],[67,70,71,245,526], [66,67,70,244,526],[67,70,244,245,526],[67,241,242,245,526],[66,67,241,244,526], [67,241,244,245,526],[66,69,71,245,526],[66,69,70,244,526],[66,69,243,244,526], [66,69,243,245,526],[66,240,242,245,526],[240,241,242,245,526],[66,240,241,244,526], [240,241,244,245,526],[66,240,243,244,526],[66,240,243,245,526],[240,243,244,245,526], [69,71,74,248,526],[70,71,74,248,526],[69,71,245,248,526],[70,71,245,248,526], [70,73,74,248,526],[69,70,73,247,526],[70,73,247,248,526],[70,244,245,248,526], [69,70,244,247,526],[70,244,247,248,526],[69,72,74,248,526],[69,72,73,247,526], [69,72,246,247,526],[69,72,246,248,526],[69,243,245,248,526],[243,244,245,248,526], [69,243,244,247,526],[243,244,247,248,526],[69,243,246,247,526],[69,243,246,248,526], [243,246,247,248,526],[72,74,77,251,526],[73,74,77,251,526],[72,74,248,251,526], [73,74,248,251,526],[73,76,77,251,526],[72,73,76,250,526],[73,76,250,251,526], [73,247,248,251,526],[72,73,247,250,526],[73,247,250,251,526],[72,75,77,251,526], [72,75,76,250,526],[72,75,249,250,526],[72,75,249,251,526],[72,246,248,251,526], [246,247,248,251,526],[72,246,247,250,526],[246,247,250,251,526],[72,246,249,250,526], [72,246,249,251,526],[246,249,250,251,526],[75,77,80,254,526],[76,77,80,254,526], [75,77,251,254,526],[76,77,251,254,526],[76,79,80,254,526],[75,76,79,253,526], [76,79,253,254,526],[76,250,251,254,526],[75,76,250,253,526],[76,250,253,254,526], [75,78,80,254,526],[75,78,79,253,526],[75,78,252,253,526],[75,78,252,254,526], [75,249,251,254,526],[249,250,251,254,526],[75,249,250,253,526],[249,250,253,254,526], [75,249,252,253,526],[75,249,252,254,526],[249,252,253,254,526],[78,80,83,257,526], [79,80,83,257,526],[78,80,254,257,526],[79,80,254,257,526],[79,82,83,257,526], [78,79,82,256,526],[79,82,256,257,526],[79,253,254,257,526],[78,79,253,256,526], [79,253,256,257,526],[78,81,83,257,526],[78,81,82,256,526],[78,81,255,256,526], [78,81,255,257,526],[78,252,254,257,526],[252,253,254,257,526],[78,252,253,256,526], [252,253,256,257,526],[78,252,255,256,526],[78,252,255,257,526],[252,255,256,257,526], [81,83,86,260,526],[82,83,86,260,526],[81,83,257,260,526],[82,83,257,260,526], [82,85,86,260,526],[81,82,85,259,526],[82,85,259,260,526],[82,256,257,260,526], [81,82,256,259,526],[82,256,259,260,526],[81,84,86,260,526],[81,84,85,259,526], [81,84,258,259,526],[81,84,258,260,526],[81,255,257,260,526],[255,256,257,260,526], [81,255,256,259,526],[255,256,259,260,526],[81,255,258,259,526],[81,255,258,260,526], [255,258,259,260,526],[84,86,89,263,526],[85,86,89,263,526],[84,86,260,263,526], [85,86,260,263,526],[85,88,89,263,526],[84,85,88,262,526],[85,88,262,263,526], [85,259,260,263,526],[84,85,259,262,526],[85,259,262,263,526],[84,87,89,263,526], [84,87,88,262,526],[84,87,261,262,526],[84,87,261,263,526],[84,258,260,263,526], [258,259,260,263,526],[84,258,259,262,526],[258,259,262,263,526],[84,258,261,262,526], [84,258,261,263,526],[258,261,262,263,526],[87,89,92,266,526],[88,89,92,266,526], [87,89,263,266,526],[88,89,263,266,526],[88,91,92,266,526],[87,88,91,265,526], [88,91,265,266,526],[88,262,263,266,526],[87,88,262,265,526],[88,262,265,266,526], [87,90,92,266,526],[87,90,91,265,526],[87,90,264,265,526],[87,90,264,266,526], [87,261,263,266,526],[261,262,263,266,526],[87,261,262,265,526],[261,262,265,266,526], [87,261,264,265,526],[87,261,264,266,526],[261,264,265,266,526],[90,92,95,269,526], [91,92,95,269,526],[90,92,266,269,526],[91,92,266,269,526],[91,94,95,269,526], [90,91,94,268,526],[91,94,268,269,526],[91,265,266,269,526],[90,91,265,268,526], [91,265,268,269,526],[90,93,95,269,526],[90,93,94,268,526],[90,93,267,268,526], [90,93,267,269,526],[90,264,266,269,526],[264,265,266,269,526],[90,264,265,268,526], [264,265,268,269,526],[90,264,267,268,526],[90,264,267,269,526],[264,267,268,269,526], [93,95,98,272,526],[94,95,98,272,526],[93,95,269,272,526],[94,95,269,272,526], [94,97,98,272,526],[93,94,97,271,526],[94,97,271,272,526],[94,268,269,272,526], [93,94,268,271,526],[94,268,271,272,526],[93,96,98,272,526],[93,96,97,271,526], [93,96,270,271,526],[93,96,270,272,526],[93,267,269,272,526],[267,268,269,272,526], [93,267,268,271,526],[267,268,271,272,526],[93,267,270,271,526],[93,267,270,272,526], [267,270,271,272,526],[96,98,101,275,526],[97,98,101,275,526],[96,98,272,275,526], [97,98,272,275,526],[97,100,101,275,526],[96,97,100,274,526],[97,100,274,275,526], [97,271,272,275,526],[96,97,271,274,526],[97,271,274,275,526],[96,99,101,275,526], [96,99,100,274,526],[96,99,273,274,526],[96,99,273,275,526],[96,270,272,275,526], [270,271,272,275,526],[96,270,271,274,526],[270,271,274,275,526],[96,270,273,274,526], [96,270,273,275,526],[270,273,274,275,526],[99,101,104,278,526],[100,101,104,278,526], 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[153,155,158,526,528],[153,155,158,527,528],[155,158,526,527,528],[153,156,158,526,528], [153,156,158,527,528],[156,158,161,526,528],[156,158,161,527,528],[158,161,526,527,528], [156,159,161,526,528],[156,159,161,527,528],[36,39,526,527,529],[36,39,526,528,529], [36,39,527,528,529],[36,159,526,527,529],[36,159,526,528,529],[36,159,527,528,529], [39,42,526,527,529],[39,42,526,528,529],[39,42,527,528,529],[42,45,526,527,529], [42,45,526,528,529],[42,45,527,528,529],[45,48,526,527,529],[45,48,526,528,529], [45,48,527,528,529],[48,51,526,527,529],[48,51,526,528,529],[48,51,527,528,529], [51,54,526,527,529],[51,54,526,528,529],[51,54,527,528,529],[54,57,526,527,529], [54,57,526,528,529],[54,57,527,528,529],[57,60,526,527,529],[57,60,526,528,529], [57,60,527,528,529],[60,63,526,527,529],[60,63,526,528,529],[60,63,527,528,529], [63,66,526,527,529],[63,66,526,528,529],[63,66,527,528,529],[66,69,526,527,529], [66,69,526,528,529],[66,69,527,528,529],[69,72,526,527,529],[69,72,526,528,529], 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